LHC

b-PU

B-20

14-0

3911

/12/

2015

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-LHCb-PUB-2014-039LHCb-PUB-2014-039

December 11, 2015

Data driven trigger efficiencydetermination at LHCb

S. Tolk1, J. Albrecht2, F. Dettori3, A. Pellegrino1

1Nikhef, Amsterdam, Netherlands2 TU Dortmund, Germany

3 CERN, Geneva

Abstract

We demonstrate in detail the trigger efficiency evaluation of the LHCb trigger systempurely on data with the so-called TISTOS method. The discussion includes an explicitoverview of the uncertainty propagation. Additionally, we present a way to reducethe systematic uncertainty of the TISTOS method by binning the phase space. Asan example, the binning is performed in the B meson phase space for B+→ J/ψK+decays.

A large sample of simulated events is used to determine the systematic un-certainties. Following the procedure discussed in this note, the trigger efficiencycan be correctly determined for any dataset of sufficient size, including a realisticdetermination of systematic uncertainties.

The developed method is used to measure the trigger efficiency of B+ → J/ψK+events in a dataset corresponding to an integrated luminosity of 3 fb−1, collected in2011 and 2012. The numerical values determined here have been used for the 3 fb−1

measurement of the branching fraction of the rare decay B0s→ µ+µ− .

c© CERN on behalf of the LHCb collaboration, license CC-BY-3.0.

http://creativecommons.org/licenses/by/3.0/

ii

Contents

1 Introduction 1

2 Estimating the trigger efficiency 12.1 Trigger categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Estimating the trigger efficiency . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Estimating the trigger efficiency uncertainty . . . . . . . . . . . . . . . . . 42.4 Binning the phase space . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Performance on simulation 63.1 The Monte Carlo sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.2 True trigger efficiency and signal separation . . . . . . . . . . . . . . . . . 63.3 Results with different phase space binnings . . . . . . . . . . . . . . . . . 83.4 Results with the best phase space binning . . . . . . . . . . . . . . . . . . 8

4 Performance on data 124.1 Data sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2 Results on the data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 Summary 14

References 14

iii

1 Introduction

This paper describes in detail the determination of the trigger efficiency using the datadriven TISTOS method.

We provide a complete overview of how the TISTOS method can be used to determinethe trigger efficiencies on data, highlight the underlying assumptions, and explicitly showhow to treat the uncertainties. Thereafter, we validate the performance of the TISTOSmethod on the simulated B+→ J/ψK+ samples, and demonstrate how the uncertaintiescan be reduced by the procedure of binning.

Finally, we determine the trigger efficiencies for B+→ J/ψK+ candidates on LHCbdata, collected in years 2011 and 2012. The LHCb detector is a forward single-armspectrometer at LHC, aimed at studies of CP-symmetry violation and rare decays in theLHC collider environment. It is discussed in more detail elsewhere [1].

The method presented here was developed in the work for the B0s,d → µ+µ− analysis andthe numbers obtained for the B+→ J/ψK+ channel are used in the 3 fb−1 measurement ofB0s,d → µ+µ− [2]. The TISTOS method, however, is applicable for any other decay channel.

2 Estimating the trigger efficiency

Various effects contribute to the efficiency with which a given decay channel can bedetected: acceptance, trigger, reconstruction, and selection efficiencies. The particlesin the candidate events must first lie within the detector acceptance, then be triggered,reconstructed, and finally pass the offline selection requirements. Each consecutive stepreduces the sample further, leaving us with a subset of all the events determined by thetotal decay rate. The overall efficiency can thus be written as a product:

�Tot = �Acc · �Trig|Acc · �Rec|Trig · �Sel|Rec (1)

The (conditional) trigger efficiency �Trig|Acc for a given decay channel is defined as thefraction of trigger accepted events, that contain a signal candidate within the acceptance:

�Trig|Acc ≡NTrig|AccNAcc

. (2)

As the detector records only events passing the trigger the number of events that thetrigger processes (NAcc) is not directly observable. A possible solution to the problem ofdetermining �Trig|Acc is based on a complete simulation of the trigger decision process. Inthis note, an alternative procedure is described that makes use of measured data sets.

In LHCb, conventionally we write the efficiencies as product of terms:

�Tot = �Trig|Sel · �Sel|Rec · �Rec|Acc · �Acc, (3)

which are different than the terms in Eq. (1), as the trigger efficiency is defined on thefinal sample of selected events:

�Trig ≡ �Trig|Sel ≡NTrig|SelNSel

. (4)

1

Figure 1: Diagram explaining the logic behind categorizing events into Trigger On Signal (TOS),Trigger Independent of Signal (TIS) and Trigger On Both (TOB) trigger categories. Note thatan event can be both TIS and TOS simultaneously.

In the remainder of this note, we will describe how this definition allows the evaluation ofthe trigger efficiency using only quantities measurable from the data samples.

2.1 Trigger categories

To estimate the trigger efficiency as given in Eq. (4) from the data itself, we split eventsaccepted by the trigger into three categories:

1. Triggered On Signal (TOS): events for which the presence of the signal is sufficientto generate a positive trigger decision1.

2. Triggered Independent of Signal (TIS): the “rest” of the event is sufficient to generatea positive trigger decision, where the rest of the event is defined through an operationalprocedure consisting in removing the signal and all detector hits belonging to it.

3. Triggered On Both (TOB): these are events that are neither TIS nor TOS; neitherthe presence of the signal alone nor the rest of the event alone are sufficient togenerate a positive trigger decision, but rather both are necessary.

The logic behind the categorization is illustrated in Fig. 1. Note that a single event canbe simultaneously TIS and TOS (TISTOS) if both the presence of the signal alone as wellas the rest of the event alone are sufficient to generate a positive trigger decision2. Using

1 For a simple trigger candidate (e.g. Track), more than around 70% (depending on the subdetector)of the online reconstructed trigger candidate hits need to be contained within the set of all the hits fromall offline reconstructed signal parts. For a composite candidate, the combination of all individual triggercandidates is compared to the set of offline candidates.

2TOB events on the other hand can be neither TIS nor TOS. As the TOB category, for the triggerdecisions under consideration, only pertains to 0.5% of the events, and these are not relevant for thedescribed TISTOS method, we do not examine them any further.

2

these event categories, we define the partial efficiencies:

�TOS ≡NTOS|SelNSel

, �TIS ≡NTIS|SelNSel

, �TISTOS ≡NTISTOS|Sel

NSel. (5)

In practice, an event is either TIS, TOS, or TOB always with respect to a specifiedselection of trigger decisions, applicable for a signal decay under consideration.

2.2 Estimating the trigger efficiency

The trigger efficiency defined in Eq. (4) can be expressed using the trigger categoriesdefined in Sec.2.1:

�Trig =NTrig|SelNSel

=NTrig|SelNTIS|Sel

×NTIS|SelNSel

=NTrig|SelNTIS|Sel

× �TIS . (6)

Henceforth, we will omit the “|Sel” subscript with the understanding that all efficienciesare defined on a sample of selected events. Eq. (6) is formally correct, but like Eq. (2),requires the knowledge of a quantity that is not directly measurable from data, the �TIS.

On the other hand, we can determine from data the TIS efficiency within the TOSsubsample. It can be evaluated from the overlap between TIS and TOS events:

�TIS|TOS =NTISTOSNTOS

. (7)

Provided that the TIS efficiency of any subsample of the triggered events is the same asthat of the whole sample of selected events, it can thus be measured on the TOS sample:

�TIS ≡ �TIS|TOS . (8)

The trigger efficiency can now be determined as

�Trig =NTrig|SelNTIS|Sel

× NTISTOSNTOS

, (9)

where all four quantities can directly be measured from data.The assumption that �TIS is independent of the chosen subsample is the main assump-

tion of this approach. Studying the validity of this assumption and its consequences is themain objective of this note.

Note, that the overall true TIS efficiency (�TIS) has to be independent of the signalsample. If the signal candidates were completely uncorrelated with the rest of the event,also �TIS|TOS would also be independent of the chosen signal sample (and Eq. (8) satisfied).This correlation, however, exists and is not negligible.

In particular B mesons are usually produced correlated with another b-hadron (asthe bb̄ quark pair is produced), therefore the “rest of the event” is very likely not to beindependent as far as momentum spectra are concerned. The trigger selection is mainly

3

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&'() &*()

&+*,)

b c

a

d

Figure 2: Redefining yields with independent terms in uncertainty calculation for selectednumber of events.

based on transverse momentum (pT ) and impact parameter (IP ) cuts, and thus introducesa correlation between the signal and the remainder of the event.

However, signal and underlying event properties can be assumed to be largely uncorre-lated in small enough regions of the signal B meson phase space. In other words, for aninfinitesimally small volume of signal phase space, Eq. (8) can be used to express the totalTIS efficiency completely in terms of quantities measurable from data

�Trig =NTrig|Sel∑

iNiSel

=NTrig|Sel∑i

N iTIS|Sel�iTIS

=NTrig|Sel∑

i

N iTIS|SelN

iTOS|Sel

N iTISTOS|Sel

. (10)

Here the summation is performed over all the bins in the phase space of the signal Bmeson.

2.3 Estimating the trigger efficiency uncertainty

Calculation of the trigger efficiency from Eq. (10) is straightforward once individual triggeryields (TRIG, TIS, TOS, and TISTOS) are known. Since the TRIG, TIS, TOS, andTISTOS yields partly contain the same events, the propagation of their uncertainties tothe efficiency needs care. To make this explicit, let us rewrite Eq. (10) as

�Trig =NTrig|Sel∑

i

N iTIS|SelN

iTOS|Sel

N iTISTOS|Sel

=NTrig|Sel∑i(bi+di)(ci+di)

di

, (11)

where we have denoted N iT ISTOS|Sel by di and the non-overlapping part of NiT IS|Sel and

N iTOS|Sel by bi and ci, respectively.

The denominator of Eq. (11) is now written in terms of independent quantities (see

4

Fig. 2) and therefore its uncertainty can be calculated as follows3

σ2NSel =∑i

σ2N iSel

=∑i

(∂N iSel∂bi

)2σ2b,i +

(∂N iSel∂c

)2σ2c,i +

(∂N iSel∂d

)2σ2d,i,

=∑i

(ci + didi

)2bi +

(bi + didi

)2ci +

(1− bici

d2i

)2di.

(12)

Analogously, the trigger efficiency can be written indicating explicitly the contributionof disjointed sets, NTrig|sel = n and Nsel = n+m:

�Trig =n

n+m, (13)

which leads to

σ2�Trig =

(m

(n+m)2

)2· σ2n +

(−n

(n+m)2

)2· σ2m

σ2�Trig =

(m

(n+m)2

)2·NTrig|Sel +

(−n

(n+m)2

)2· (σ2NSel −NTrig|Sel)

(14)

where in the last step we have used the fact that σ2Nsel = σ2n + σ

2m.

2.4 Binning the phase space

The phase space of the B meson can be parameterized by the transverse and longitudinalmomenta.

At first we calculate the binning boundaries for both variables independently, suchthat about the same number of TISTOS events fall into each bin 4.

For both dimensions independently, the number of events in the bins with the optimizedboundaries agrees within a few percent. After applying the independently optimized binboundaries on the 2 dimensional phase space, the number of events that fall in eachbin show a greater variance. This is due to the fact that transverse and longitudinalmomentum are not independent variables.

The slight correlation between the chosen variables does not jeopardise the performaceof the TISTOS method, where the underlying assumption is that TIS and TOS decisionsare uncorrelated for the events within the same small region of phase space.

3Here we assume the yield uncertanties follow a Gaussian distribution and use the first-order Taylorseries approximation for the uncertainty propagation. For the Gaussian assumption to be valid, the yieldsin each bin need be large enough ( O(10)).

4TISTOS is the category with the smallest statistics and therefore influences the method performancethe most. Dividing events equally between the bins minimizes the chances of encountering a bin with toofew or no statistics.

5

3 Performance on simulation

In this section, we will demonstrate how the previously described TISTOS method (seeSec.2) performs on the simulated events. The TISTOS result are compared to the trueefficiency of the simulated sample.

3.1 The Monte Carlo sample

The pp interactions are simulated using the Monte Carlo (MC) technique. Only those ppinteractions are accepted where one or more5 signal events (i.e. B+→ J/ψK+ ) lie withinthe LHCb detector acceptance. The accepted MC events are next processed by the LHCbtrigger, reconstruction, and selection algorithms just as the events from real pp collisions.

Note that accepted MC events contain also accompanying decays besides the signal.Thus, it may well happen that some of those mimic the signal well enough to pass all thefollowing signal selection criteria.

We have produced two MC samples for B+→ J/ψK+ decay channel with slightlydifferent detector configurations and sample sizes. The smaller sample contains 127× 103generated events in the detector acceptance (MC127k in the following) and it is generatedwith the same detector configuration as used during the data taking in May and June, 2012.The larger MC sample of 1000× 103 events (MC1000k) uses the detector configurationfrom July, August and September, 2012.

For both samples, the pp interactions have been simulated assuming a beam energy of4 TeV, an average number of interactions per crossing ν = 2.5, which corresponds to anaverage number of visible interactions per crossing µ = 1.75.

3.2 True trigger efficiency and signal separation

The true trigger efficiency from the MC is an important benchmark in our study. Itprovides a reference point and allows us to test how well the TISTOS method performs.Eventually, it makes it possible to evaluate the bias of the TISTOS method and use it as asystematic uncertainty assigned to the approach.

On MC, the trigger can be emulated in a way that also the selected events which donot pass the trigger requirements are kept. Thus, the trigger efficiency defined in Eq. (4)can be evaluated directly from NTRIG/NSEL. We will refer to this quantity as true triggerefficiency.

Calculation of any trigger efficiency relies on the methods of separating the signalcandidates from the rest. In this note we consider two different methods to determine thesignal yield in the samples: Sideband Subtraction (SB) and a Maximum Likelihood (ML)fit. In the following, we will demonstrate the performance of the methods with respectto each other, and also with respect to the truth information available in the simulatedevents.

5The fraction of events with more than one entry is at 0.1% level.

6

SB serves as the main signal yield determination method in our study. This is mainlybecause of its robustness when dealing with bins containing fewer events, but also becauseof the possibility to perform SB on the whole phase space (i.e. all the bins) at once.

SB is performed on the B meson invariant mass distribution, where the B mesoninvariant mass is calculated after using a constraint on the J/ψ mass. We look at a masswindow of ± 100 MeV/c2 around the PDG mass, where the events that lie away morethat 55 MeV/c2 from the mean mass value form the sidebands. The yield in the sidebandsis extrapolated over the whole mass window, and thereafter subtracted from the totalyield in the mass window.

For the ML fit, we build first a probability density function (p.d.f.) describing the Bmeson invariant mass distribution. The RooFit package [3] performs the evaluation of thetotal likelihoods for all the events in the data sample. MINUIT minimizer [4] is used to findthe set of parameter values that maximise the total likelihood calculated by RooFit.

The invariant mass model p.d.f. for B+ → J/ψK+ decay consists of two Gaussianswith a shared mean, but different (independent) widths. The background model hastwo parts, first an exponential to describe the combinatorial background, and secondlya Crystal Ball function to describe the events where a pion has been mis-identified as akaon. This mis-identified component has a fixed mean with respect to the signal meanmass value.

As the third option, in the simulated sample we can use the MC matching procedure toselect the true signal events. The matching procedure relies on the MC truth informationfor every particle in the simulated event. In particular, for B+ → J/ψK+ to be matchedas a signal event, the particles must first not be misidentified, and secondly, they need tobe properly linked in the decay chain (e.g. the J/ψ needs to originate from the B+ decay,etc.).

The events that pass the MC matching criteria (i.e matched events), will form thematched sample. Note that even the MC truth matching process that provides MC truthinformation for the particles is not 100% efficient6. This means that not all the signalcandidates reside in the matched sample.

For the comparison of the methods, we apply both SB and ML and calculate the truetrigger efficiency on (i) the matched sub-sample, (ii) the un-matched sub-sample, and (iii)the total simulated sample.

The results are shown in Table 1, whereas the result from the matched sample isassumed to be the closest to the true value.

The SB and ML results are in all the cases almost indistinguishable. However, thetrigger efficiency between the matched and the un-matched sample, that has much morebackground events compared to signal events, differs significantly. The results from thetotal sample are in good agreement with the true efficiency in the matched sample.

From this we conclude that SB and ML are capable of separating the signal yield onthe total sample and it is sufficient to apply SB/ML directly on the total MC sample

6The mistakes can happen because of possible wrong links between the true simulated and reconstructeddetector hits.

7

without requiring truth matching. Thus, �true is chosen as the benchmark in the followingMC studies.

3.3 Results with different phase space binnings

It has become a common practice in the LHCb collaboration to use TISTOS method inthe trigger efficiency determination directly from the data. Even so, binning Eq. (9) (orEq. (5) for TOS efficiencies) in the phase space is not always implemented.

This results in a considerable, and furthermore, unnecessary increase in the assignedsystematic uncertainty to the trigger efficiency estimation. On MC127k sample, the TISTOSmethod without binning gives more than 5% higher result when compared to the trueefficiency in the same sample (Tab. 2).

The relative bias of the TISTOS method (and thus the systematic uncertainty) canbe significantly reduced by treating different regions of phase space independently andcombining the results into an overall efficiency of the sample.

The TISTOS method was applied with increasing number of bins on both MC samples.Comparing the efficiencies with different binning schemes with respect to the true efficiencyof the sample, one clearly sees the TISTOS result converging to the true efficiency valuewhen the number of bins in the B meson phase space increases (Fig. 3 and 4, for MC127kand MC1000k, respectively).

As a cross check, we performed an identical study using the ML method instead of SB.The comparison between the SB and MLL on MC127k sample is shown in .

For a lower number of bins, the results are in good agreement. As the number of binsincreases, the individual bins contain less and less statistics. Eventually, the ML fit willnot have enough statistics to separate the signal and becomes unreliable (Fig. 5). In therest of the note we will use SB, yet it is important to note that ML perform equally wellgiven sufficient statistics7.

3.4 Results with the best phase space binning

We define the best binnning scheme to be a compromise between the smallest relativebias and the statistical uncertainty of the efficiency. Hence the optimal binning scheme

7Moreover, for a number of signal channels the Sideband Subtraction might not be an option (e.g.because of additional peaking components in the background distribution).

Table 1: True unbinned trigger efficiency on matched (�match), not-matched (�notmatch), and onthe whole MC127k sample (�true).

Signal separation �match �notmatch �trueSideband subtraction 87.39± 0.22% 84.44± 1.61% 87.32± 0.22%MLL fit 87.37± 0.22% 85.56± 1.54% 87.32± 0.22%

8

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bins: 1z

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Figure 3: The true trigger efficiency (red line), efficiency calculated with the TISTOS method,and the relative bias of the TISTOS efficiency in the MC127k sample depending on the numberof B meson pZ and pT bins.

depends slightly on the sample size. The dependence is studied on using two MC sampleswith similar configurations yet different sizes, MC127k and MC1000k.

For the smaller sample, MC127k, the best results are obtained with 4 bins in pz and5 in pT . The relative bias could be reduced considerably, from (5.5 ± 1.5)% down to(0.5± 0.4)%.

The best binning on the larger sample, MC1000k, has 4 bins in pz and 9 in pT . OnMC1000k the relative bias can be reduced from (3.9 ± 0.1)% down to (0.25 ± 0.1)%(Tab. 3).

From comparing the best binning schemes on the smaller and larger MC sample, (4

Table 2: Efficiency evaluated with the TISTOS method (�T isTos) and its relative bias with respectto the �true (Bias(�)).

Signal separation method �true �T isTos Bias(�)

Sideband subtraction 87.322± 0.22% 92.622± 1.523% 5.723± 3.26%MLL fit 87.324± 0.22% 92.337± 1.532% 5.429± 3.27%

9

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Figure 4: The true trigger efficiency (red line), efficiency calculated with the TISTOS method,and the relative bias of the TISTOS efficiency in the MC1000k sample depending on the numberof B meson pZ and pT bins.

bins in pz and 9 in pT on MC1000k, instead of 4 and 5 on MC127k) we conclude that theeffect of the sample size on choosing the best binning is not significant.

In other words, we can use the best binning scheme taken from a respective MC sampledirectly on the data sample with a different size Also, the study shows that the changein the number of bins has a relatively small effect on the bias when the number of binsexceeds 3 in both dimensions.

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Figure 5: The TISTOS trigger efficiency calculated on MC127k depending on the number of Bmeson pZ and pT bins. The black points represent results with sideband subtracted (SB) signalyields, the red points from the signal yields from maximum likelihood (MLL) fit.

Table 3: Efficiency evaluated with the TISTOS method (�T isTos) and its relative bias with respectto the �true (Bias(�)) with no binning and the best chosen binning schemes.

Sample / Binning (pZ , pT ) �true �T isTos Bias(�)

MC127k/ No binning 87.3± 0.2% 92.6± 1.3% 5.7± 0.3%MC127k/ 4x5 87.3± 0.2% 87.8± 2.2% 0.5± 0.4%

MC1000k/ No binning 87.6± 0.1% 91.2± 0.5% 3.9± 0.1%MC1000k/ 4x9 87.6± 0.1% 87.9± 0.7% 0.25± 0.1%

11

4 Performance on data

The TISTOS based procedure and the binning developed in the previous sections is appliedon the B+ → J/ψK+ candidates in the full LHCb data set from years 2011 and 2012.The trigger efficiencies determined here are also used for the analysis of the rare decaysB0s,d → µ+µ−.

4.1 Data sample

The results described in this section are obtained using the pp collision data collectedby LHCb in years 2011 and 2012 at a centre-of-mass energy of

√s = 7 TeV ( 1 fb−1 of

integrated luminosity) and 8 TeV ( 2 fb−1), respectively.In 2011 the LHC machine started the operations from a a peak luminosity L ∼ 1.6×1032

cm−2 s−1 with 228 bunches (180 bunches colliding in LHCb) and an average number of ppvisible interactions per crossing of µ ∼ 2.5. After the first 10 pb−1 collected by LHCb, themachine moved to the 50 ns bunch scheme and kept increasing the number of bunchesby 144 every three fills, by reaching 1380 circulating bunches (1296 colliding bunches inLHCb). Since then the peak luminosity in LHCb was continuously levelled in order not toexceed 3− 3.5× 1032 cm−2 s−1 corresponding to an average < µ >∼ 1.5.

During 2012, the data taking conditions were very stable. The first 100 pb−1 werecollected while the machine was ramping up the luminosity to 4× 1032 cm−2 s−1, at whichthe remaining 2 fb−1 were taken. The average number of pp visible interactions per crossingwas very stable at µ ∼ 1.6. All data were recorded with a LHC bunch spacing of 50 ns.

4.2 Results on the data

The trigger efficiencies measured in this section are obtained for the combined physicsdecision of each trigger level. Physics decision will be positive, if the event was triggeredby any of the physics lines in the trigger level. The combined trigger decision is positiveonly if the events has a positive physics decision from all the three trigger levels.

Whereas the trigger configurations are slightly different between the years 2011 and2012, and also between the simulated samples and the recorded ones8, the bias andsystematic uncertainty determined in Sec. 3 is assumed to be independent of these smallchanges.

Different binning schemes have been studied on a large MC sample with similarconditions to the 2012 data taking period. The results and the choice for the bestperforming binning are described in Sec. 3.3, where we have also evaluated the relativebias of the TISTOS method for the best binning (4 bins in pZ , 9 in pT ) to be 0.25%.

The binning scheme obtained on the MC is applied on both 2011 and 2012 data samples,whereas the estimated relative bias is used as a systematic uncertainty on the final result.

8For practical reasons, the trigger configuration in data is adjusted over the year to adjust to theboundary conditions like available delivered luminosity, farm size or physics focus. In MC, only thedominant configuration is simulated.

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The trigger efficiencies from the binned TISTOS method compared to the unbinnedTISTOS method are in general by 4− 5% lower on data (Tab. 4). The same pattern wasobserved on the simulated samples (Tab. 3).

We can reduce the total uncertainty of the TISTOS method on the 2011 and 2012 datasamples from 4% down to 0.3% by binning the B meson phase space.

Table 4: Trigger efficiencies in the data with and without binning the B meson phase space.

Binning �T isTos ±Abs.Stat.Unc. ±Abs.Syst.Unc. Rel.Syst.Unc.Data: 2011 S20r1No binning 92.9% 0.5% 3.6% 3.9%4x9 87.8% 0.6% 0.2% 0.25%

Data: 2012 S20No binning 92.0% 0.3% 3.6% 3.9%4x9 87.8% 0.4% 0.2% 0.25%

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5 Summary

Trigger efficiencies can be determined from the measured data with the TISTOS method,provided the trigger performs the necessary classification of the events. Furthermore, thereis a way to reduce the systematic uncertainty of the method that mainly arises from thecorrelations between the trigger classifications.

As has been demonstrated on the simulated B+→ J/ψK+ data samples, binning thephase space of the B meson in the transverse and longitudinal momentum plane reducesthe systematic bias of the TISTOS method considerably: from a relative 4% to 0.3% onthe 2012 MC sample.

The residual relative bias determined is recommended to be added as relative systematicuncertainty to the trigger efficiency determined with the binned TISTOS method, whenusing the best determined binning scheme.

The TISTOS method with the chosen best binning scheme of 9 B meson pT bins and 4B meson pZ bins has been applied on the full 2011 and 2012 data sets from LHCb. Thephysics decision trigger efficiency for B+→ J/ψK+ candidates in 2011 is

�TRIG2011 = 87.8%± 0.6%(stat)± 0.2%(syst),

and in 2012

�TRIG2012 = 87.8%± 0.4%(stat)± 0.2%(syst).

The results agree well to each other, and are dominated by the statistical uncertaintywhen using the phase space binning for the TISTOS method.

References

[1] LHCb collaboration, A. A. Alves Jr. et al., The LHCb detector at the LHC, JINST 3(2008) S08005.

[2] LHCb collaboration, R. Aaij et al., Measurement of the B0s → µ+µ− branching frac-tion and search for B0 → µ+µ− decays at the LHCb experiment, arXiv:1307.5024.submitted to Phys. Rev. Lett.

[3] W. Verkerke and D. P. Kirkby, The RooFit toolkit for data modeling, eConf C0303241(2003) MOLT007, [arXiv:physics/0306116].

[4] F. James, MINUIT Function Minimization and Error Analysis: Reference ManualVersion 94.1, .

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http://dx.doi.org/10.1088/1748-0221/3/08/S08005http://dx.doi.org/10.1088/1748-0221/3/08/S08005http://xxx.lanl.gov/abs/1307.5024http://xxx.lanl.gov/abs/physics/0306116

IntroductionEstimating the trigger efficiencyTrigger categoriesEstimating the trigger efficiencyEstimating the trigger efficiency uncertaintyBinning the phase space

Performance on simulationThe Monte Carlo sampleTrue trigger efficiency and signal separationResults with different phase space binnings Results with the best phase space binning

Performance on dataData sampleResults on the data

SummaryReferences